Essential Ideas for Section 1.4
One-to-one Correspondence Two sets A and B are said to be in a one-to-one
correspondence if we can find a pairing so that:
(1) Each element of A is paired with precisely one element
of B; and
(2) Each element of B is paired with precisely one element
of A.
Finite and Infinite
A set is infinite if it can be placed in a one-to-one correspondence with a proper subset of itself. A set is finite if it is not infinite.
Fundamental Counting Principle
If task A can be performed in m ways, and after task
A is performed, a second task B can be perfomed in n
different ways, then the fundamental counting principle is that
task A followed by task B can be performed in mn
different ways.